Delete the damaged/corrupt "Install macOS xxxxxx" app from the Applications folder and empty the Trash. Try downloading the installer again. If the size of the "Install macOS xxxxx" app is only about 20MB instead of 5-6GB, then you may also need to delete the "/macOS Install Data" from the root of the drive if only the small 20MB stub installer is present.
A memory upgrade will not give you much of a performance boost. An SSD upgrade is what will give the biggest performance boost if you can get a good SSD. Unfortunately not all SSDs are created equal...there are a lot of slow & junk SSDs out there. However, the original internal Apple hard drive is likely worn out or even failing now which will easily cause the iMac to lose performance since the hard drive was never fast to begin with.
It is relatively easy to determine if you need more memory. You use the computer normally and while you are doing the largest workload, you check the Memory tab of Activity Monitor. Look at the Memory Pressure graph. If it is red, then you need more memory for that particular workload unless you can close some apps instead. If the graph is yellow, then you are borderline on memory. If the graph is green, then check the "Compressed" and "Swap Used" items. If either of these two items are using GBs, then it may mean you need a bit more memory. Otherwise, you have enough memory and adding more is just a waste of money. If you need any memory, then get it from OWC or Crucial since Macs are very picky about the memory they use....even then, only get the exact part numbers shown as recommended compatible by using the tools on their respective websites to identify compatible memory for that specific computer.
Upgrading to an SSD is the best option to increase performance. An external SSD would be easiest since these iMacs are difficult to open and can be easily damaged. If you want to replace the internal drive, then OWC is the best option since they have kits that may be necessary to fit an SSD and installation videos.
